The free weekend means anyone can download/install the game and play it without having to purchase it this weekend. They do this occasionally with different games to let people try them out. If you look next to the game in your Steam Library it should have a little countdown timer, something like 3 days 15 hours, etc.
During this free weekend you can also buy the game for $9.99 which will allow you to continue playing after the weekend ends. If you wait and don't decide to buy until say Wednesday you'll have to pay $19.99.
Either way you can play this weekend and not pay a dime.
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